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A room is approximately shaped like a golden rectangle. It's length is 23 ft. What is the rooms width? Write your answer in simplified radical form and rounded to the nearest tenth of a foot. Note that the ratio of the length to the width of a golden rectangle is (1+ ^5):2

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calculista

Answer:

[tex]W=\frac{-23+23\sqrt{5}}{2}\ ft[/tex]

[tex]W=14.2\ ft[/tex]

Step-by-step explanation:

Let

L ----> the length of rectangle in ft

W ----> the width of rectangle in ft

we know that

[tex]\frac{L}{W} =\frac{1+\sqrt{5}}{2}[/tex] -----> equation A

[tex]L=23\ ft[/tex]

substitute the value of L in the equation A

[tex]\frac{23}{W} =\frac{1+\sqrt{5}}{2}[/tex]

[tex]W=\frac{46}{1+\sqrt{5}}[/tex]

Simplify

[tex]W=\frac{46}{1+\sqrt{5}}(\frac{1-\sqrt{5}}{1-\sqrt{5}})[/tex]

[tex]W=\frac{46(1-\sqrt{5})}{1-5}[/tex]

[tex]W=\frac{46-46\sqrt{5}}{-4}[/tex]

[tex]W=\frac{23-23\sqrt{5}}{-2}[/tex]

[tex]W=\frac{-23+23\sqrt{5}}{2}[/tex]

[tex]W=14.2\ ft[/tex]

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